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Example of a Triad Solution
A boundary survey is required of Lot "B" (below)
to re-establish the missing corners. The coordinates of the map
corners and the found monuments are retrieved from an ASCII (plain
text) data file. See the following explanation of a sample printout
(the Program Manual contains a detailed example)
********************** STEP
ONE: INITIAL SOLUTION *********************
The record map is best fit to the five found
monuments using the coordinates of common points. The largest
error or residual is from the calculated position of #403 to the
found monument #3 shown below as *181° in azimuth (S 1°W) 0.81'.
The best rotation and scale is determined with a 68% probable
error indicated by the Standard Deviation.
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Map Pts
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Field Pts
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Rectangular Differences
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Polar Differences
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System 1 to
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System 2
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North (Lat)
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East (Dep)
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N. AZIM
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DIST
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402
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2
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-.004
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+.104
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92°
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.104
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*403
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3
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-.809
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-.010
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*181°
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*.809
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404
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4
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+.475
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+.447
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43°
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.653
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406
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6
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+.225
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-.137
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328°
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.263
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407
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7
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+.113
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-.404
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286°
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.419
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Standard Deviation of the latitudes and departures
= 0.39
Scale Factor = 1.00004129 Standard
Deviation = .00038340
Rotation = - 1° 09' 54.3" Standard
Deviation = 0° 01' 19.1"
********************* STEP TWO:
BLUNDER DETECTION*********************
This option determines the largest error that
would remain after rejecting each of the found monuments indicated
below. Rejecting #3 will reduce the largest error in the Initial
Solution from 0.81'at #3 (above) to *0.13' at #6. The rotation
and scale that would result follow on the same line.
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REJECT
POINT #
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MAXIMUM RESIDUAL
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ROTATION
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SCALE
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N. AZIM
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DIST -> PT #
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2
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181°
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.79
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3
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-001° 10' 07"
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1.000059
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* 3
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138°
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*.13
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* 6
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-001° 09' 29"
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.999336
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4
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88°
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.45
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2
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-001° 10' 50"
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1.000368
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6
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180°
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.72
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3
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-001° 09' 42"
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1.000090
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7
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181°
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.66
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3
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-001° 09' 21"
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1.000237
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* It can be seen by inspection that the best solution
will be obtained after rejecting #3. Triad will automatically
search and report this fact.
********************* STEP THREE:
FINAL SOLUTION ********************
Point #3 is rejected by setting the pair 403,
3 "FREE". The solution is re-computed to best fit the
remaining monuments. The calculated corner positions now fall
between 0.06' to 0.13' of the found monuments as shown below.
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Map Pts
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Field Pts
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Rectangular Differences
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Polar Differences
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System 1 to
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System 2
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North (Lat)
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East (Dep)
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N. AZIM
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DIST
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402
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2
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+.055
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-0.055
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314°
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0.08
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403
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3
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-1.611
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-.021
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180°
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1.61 FREE
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404
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4
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+.037
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+.049
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53°
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.06
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406
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6
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-.096
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+.085
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138°
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.13
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407
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7
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+.004
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-.079
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272°
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.08
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Root Mean Square of the North and East Residuals
= 0.06 (#3 excepted)
Scale Factor = 0.99933648 Standard
Deviation = .00009303
Rotation = - 1° 09' 29.9"
Standard
Deviation = 0° 00' 19.2"
***************** STEP FOUR:
CREATE NEW COORDINATES *****************
New coordinates are computed for mapping and
staking. To avoid conflicts in the coordinate file a value of
100 is added to the map point numbers for the new points computed
in the field coordinate system.
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Map Coordinates (input)
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Field Coordinates (output)
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PROBABLE ERROR
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PT#
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NORTH
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EAST
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PT#
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NORTH
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EAST
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403
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2748.923
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5023.754
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503
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19315.877
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39960.416
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.13
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405
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3350.321
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5042.829
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505
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19917.139
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39967.325
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.07
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Note, there is an expectation at the 68% level
of confidence that the computed positions of corners #403 and
#405 are radially within 0.13' and 0.07'. This is useful in determining
the reliability of the position or for an estimated corner search
radius.
SYSTEM REQUIREMENTS:
SYSTEM REQUIREMENTS: WINDOWS 95, 98, ME, 2000, XP & NT - PURCHASE
PRICE $445.00
COPYRIGHT 1990-2002 MCGEE SURVEYING CONSULTING
Tel. 805-964-3520
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